10x-2/5x-4=0

Solution for 10x-2/5x-4=0 equation:

10x-2/5x-4=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


10x*5x-4*5x-2=0

Wy multiply elements

50x^2-20x-2=0

a = 50; b = -20; c = -2;
Δ = b2-4ac
Δ = -202-4·50·(-2)
Δ = 800
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20\sqrt{2}}{2*50}=\frac{20-20\sqrt{2}}{100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20\sqrt{2}}{2*50}=\frac{20+20\sqrt{2}}{100}
$